Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks

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	Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks
其他题名	Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks
	Zheng Weizhe
	2015-01-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	58 期号:3 页码:565-632
摘要	Laszlo and Olsson constructed Grothendieck's six operations for constructible complexes on Artin stacks in etale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. We give a more direct construction of the six operations for complexes on Deligne-Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed by Zheng (2014). As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and l-adic coefficients.
其他摘要	Laszlo and Olsson constructed Grothendieck's six operations for constructible complexes on Artin stacks inetale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves.We give a more direct construction of the six operations for complexes on DeligneMumford stacks without the finiteness assumption and establish base change theorems in derived categories.One key tool in our construction is the theory of gluing finitely many pseudofunctors developed by Zheng(2014).As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks.We include both torsion and ?-adic coefficients.
关键词	SHEAVES Deligne-Mumford stack etale cohomology six operations pseudofunctor Lefschetz-Verdier formula
收录类别	CSCD
语种	英语
资助项目	[China's Recruitment Program of Global Experts] ; [National Natural Science Foundation of China] ; [Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences] ; [National Center for Mathematics and Interdisciplinary Sciences] ; [Chinese Academy of Sciences]
CSCD记录号	CSCD:5386945
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52672
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Zheng Weizhe. Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks[J]. SCIENCE CHINA-MATHEMATICS,2015,58(3):565-632.
APA	Zheng Weizhe.(2015).Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks.SCIENCE CHINA-MATHEMATICS,58(3),565-632.
MLA	Zheng Weizhe."Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks".SCIENCE CHINA-MATHEMATICS 58.3(2015):565-632.